Osb = Oriented strand board. Relatively large flakes and strands of wood laid down and glued/pressed together to make sheets. Used in place of plywood for floors and exterior and roof sheething. Strong stuff that is cheaper than plywood because it doesn't require pristine veneer layers. Chips are "oriented" in alternating directions, like plywood veneers are, for added dimensional stability and strength in shear.
MDF= "medium density fiberboard" is a high grade particle board. Made from fine dust-like particles it is very dimentionally stable and doesn't shrink and swell or warp as much as real wood. Not for structural applications. Can be used for a substrate for painted items and some casework. It usually has very smooth faces that are great for paint. Mostly interior uses. If it gets wet it turns to goo eventually. HDF is I think High density fiberboard that is harder. Sometimes it is difficult for dIY'ers to get a hold of this stuff.